General comments

Field measurements of a nacelle mounted Doppler lidar are used to train and validate a data-driven wake model for yawed wind turbines in comparison to an analytical wake model.

The research question is relevant to the field of wind energy. The descriptions of the measurement campaign and the methods are missing some information. More consideration should be given to the assumptions of the analytical model and how they might affect its results. The presentation of the results is good and the conclusions drawn are reasonable. I believe my comments can be addressed by the authors and then I would recommend accepting the manuscript.

Main comments:

1) One of the conclusions is that the data-driven wake model performs better than the analytical wake model under high wind shear or yaw misalignment of the wind turbine. The analytical model was designed for the far-wake, but the measurements are taken at x=4D, which might be still within the near-wake for some conditions. Therefore, I believe the authors should make an effort to investigate if the cases with large errors of the analytical model might also be linked to applying the analytical model to the near wake for which it is not designed (see specific comments for lines 342-344).

2) The observed upward displacement of the wake center is crucially dependend on the lidar's orientation (especially the tilt). However, the manuscript does not provide any information on the accuracy of the tilt/pitch/roll sensors used to correct the lidar measurements nor how they were corrected exactly (see specific comments for lines 200-204 and 360-363).

Specific comments

Line 71/72: Provide a citation for the model comparison with LES.

Line 90: Provide more details on the lidar used.

Line 110: What was the surface coverage at the measurement site? Are there buildings, trees, forests, or other features that might affect the flow at the height of the measurements?

Line 134: I believe “time / temporal averages” might be a more clear description than “point-wise averages”.

Line 149-151: Stating the elevation angles explicitly would make it easier to get an overview of the lidar scans (or a schematic of the scan).

Line 169: For consistent language to the previous text consider using “PPI scan” instead of “scan” and “10-minute window” instead of “data set”.

Line 179: It is not clear to me what the maximum would be here.

Line 200-204: What was the accuracy of the tilt and pitch provided by the GPS sensor? And what was the temporal resolution? Lastly, how were the lidar scans corrected exactly? Was each measurement point corrected individually or was the correction applied on average for a PPI / a cycle of five PPIs / a 10-minute window?

Line 232-234: The medians given in the text and the medians given in Fig. 4 are different from (I assume that mu is the median).

Line 236: I assume "normal" means here that the values fall within the typical range for the ABL and not the normal distribution in the statistical sense (maybe rephrase).

Line 245-251: It seems unintuitive to me that the quantification of the wake characteristics from the lidar measurements is described in the section of the data driven model.

Line 249: The azimuth-opening angle of PPI scans is 70°, but the wake will take up only a small part of this window. Which of the vertical slices are selected for the vertical 1D Gaussian fit? (Or how are fits rejected, which are outside of the wake?)

Line 329: Consider clarifying that the training time is the computation time of the training process (it could be misunderstood as the time window of the training data set).

Line 341: Can you provide details on the model physics (e.g. the model equations would be helpful)? The provided reference seems to focus on technical aspects of the implementation.

Line 342-344: If using a far-wake model for the near-wake, one would expect to see bad results. The correlation between the observed velocity deficit and the Gaussian fit (which are already done for determining the wake characteristics as described in Sect. 3.1) could be used to identify if the conditions are met to apply the model. It should be possible to identify and remove 10-minute windows, which do not fulfill the model requirements. Alternatively, the correlation could provide a metric to investigate a dependency of large errors to a non-Gaussian velocity deficit in a manner similar to Fig. 12.

Line 346: Have those tuning parameters physical meanings like a wake growth rate (since k is frequently used for this)?

Line 352-353: Based on the description of the Multiple 1D Gaussian method, it is not yet clear to me how the vertical and horizontal displacement of the wake center are exactly determined. For example: for each 1D Gaussian fit along a PPI scan (horizontal), a lateral wake displacement is determined (five in total, if no PPI scan was rejected due to the CNR). Are they then averaged or is a specific one selected?

Line 360-363: This result for the vertical wake displacement is depends on the precise orientation of the lidar. If the wind turbine and subsequently the lidar are tilted backwards due to tower bending, the lidar data would suggest that the wake is displaced upwards. Bromm et al (2018) have a discussion on this issue. Are the pitch, roll, and tilt readings from the GPS sensors accurate enough to exclude this issue here? If the leveling of the lidar is not an issue, it might be further interesting to test if the upward displacement of the wake center holds for both wind direction sectors to exclude topographical effects.

Bromm, M, Rott, A, Beck, H, Vollmer, L, Steinfeld, G, Kühn, M. Field investigation on the influence of yaw misalignment on the propagation of wind turbine wakes. Wind Energy. 2018; 21: 1011– 1028. https://doi.org/10.1002/we.2210.

Line 431: I am confused here. What are the transparent markers in other panels indicating? I used search function and the word transparent does not show anywhere else. The legend of Fig. 13 also gives no hint.

Line 461: A note should be added here that TI_s serves only as an input for DART and biases are acceptable, because turbulence intensity from a cup anemometer has many problems.

Technical corrections

Line 10: I am not sure that SCADA is a common abbreviation that needs no introduction.

General: Some abbreviations are introduced multiple times (e.g. DART, GCH). Others are not introduced at all (e.g. NREL, FLORIS).

Sect. 1-3 in general: I believe a more liberal use of paragraph breaks could be made, when the text moves on to a new thought or new topic.

Line 191/192: Maybe: “A flow distortion due to the tower structure affecting the measurements of the met mast occurs for the wind direction sector between X° and Y°, which is not considered in this study (Sect. 2.1). The wind directions analyzed here are assumed to be undisturbed.”

Line 251: Maybe: “The same method is applied” instead of “the same thing is done”.

General comments

This manuscript contributes to the wind energy field by assessing the quality and performance of a data-driven wake model through a validation experiment with field data.

The authors provide a detailed overview of the measurement campaign and methods used for assessment of the wake models, as well as an extensive consideration of other literature. The results appear to support the conclusion that the presented data-drive wake model outperforms the gaussian-curl hybrid model in terms of prediction of available downstream power. It should be noted that this is only for a downstream distance of four rotor diameters and for a limited range of yaw angles.

Specific comments

The authors refer to the potential of the data-driven model as “enormous” and “huge”. This appears to be an overstatement in light of the presented results. Suggest to reduce the exaggeration of potential and make more note in the conclusions of the limitations of this data-driven approach.

The model is claimed to be retrainable, however doing so requires further lidar measurements. Same goes for predictions at other downstream distances. The impact of this requirement on field application needs more emphasis. Additionally, the achieved range of yaw misalignment is considerably smaller that what is used in other literature for wake redirection. It is only briefly noted that the model does not generalise outside of the input range in training data. This limits the potential for application in wake steering control.

In Section 2.2, concerning the choice of lidar angular velocity and number of PPI scans, it is noted that “too few cases are studied for the statistics to converge”. Would that not make the entire comparison invalid? The need to motivate the choice of scanning strategy is clear, but these results appear statistically insignificant?

Technical corrections

• Shorter paragraphs would improve structure and readability.
• Suggest to revise structure, there is quite some inconsistency in length and use of sections / subsections / paragraphs.
• Introduction mentions “free-field” experiments, would this not just be a field experiment?
• Figure 1: colours of topographic map need a colourbar
• Figure 7: black line is not referenced. What is it?
• Section 4.2: Numerous references are made to the width of normal distribution fits. Consider quantifying by noting standard deviation of fit?
• Figure 9: indicate the fit quality for the linear fit of trend lines. The associated claim of a “clear” dependency needs more support given the scatter in the data. (ln. 378)

Please see attached pdf.